$\lim_{x\to \frac{\pi}{4}}\cos(x)=?$ Choose 1 answer: Choose 1 answer: (Choice A) A $\dfrac{1}{2}$ (Choice B) B $1$ (Choice C) C $\dfrac{\sqrt{2}}{2}$ (Choice D) D The limit doesn't exist.
$\cos(x)$ is continuous on all points in its domain, and its domain is all real numbers. Therefore, we can find $\lim_{x\to \frac{\pi}{4}}\cos(x)$ by direct substitution. $\begin{aligned} \cos\left(\dfrac{\pi}{4}\right)&=\dfrac{\sqrt{2}}{2} \end{aligned}$ $\lim_{x\to \frac{\pi}{4}}\cos(x)=\dfrac{\sqrt{2}}{2}$